On µ-lifting Modules

  • Enas Mustafa Kamil Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq
  • Wasan Khalid Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq
Keywords: µ-coessential sub modules, µ-lifting modules

Abstract

Let R be a ring with identity and let M be a left R-module. M is called µ-lifting modulei f for every sub module A of M, There exists a direct summand D of M such that M = D D', for some sub module D' of M such that AD and A D'<<µ D'. The aim of this paper is to introduce properties of µ-lifting modules. Especially, we give characterizations of µ-lifting modules. On the other hand, the notion of amply µ-supplemented iis studied as a generalization of amply supplemented modules, we show that if M is amply µ-supplemented such that every µ-supplement sub module of M is a direct summand, then M is µ-lifting module. Finally, we give some conditions under which the quotient and direct sum of µ-lifting modules is µ-lifting.

Published
2019-02-28
How to Cite
Kamil, E. M., & Khalid, W. (2019). On µ-lifting Modules. Iraqi Journal of Science, 60(2), 371-380. Retrieved from https://ijs.uobaghdad.edu.iq/index.php/eijs/article/view/627
Section
Mathematics